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Hardware-wise: PowerPC is a microprocessor developed mainly by the three developing companies Apple, IBM, and Motorola. It is built with reduced instruction-set computer (RISC) which speeds-up the operation of MIPS (million instructions per second). PowerPC is mainly based on IBM’s earlier Power architecture because it has a similar RISC instruction set for microprocessors.

Intel and AMD CPU's are based on CISC architectures. Typically CISC chips have a large amount of different and complex instructions. The philosophy behind it is that hardware is always faster than software, therefore one should make a powerful instructionset, which provides programmers with assembly instructions to do a lot with short programs.
In common CISC chips are relatively slow (compared to RISC chips) per instruction, but use little (less than RISC) instruction

PPC Macs refers to the generation of Macintosh computers created in the mid to late 1990s through to 2006 that used PowerPC RISC based chips made by IBM or Motorola. That last PowerPC based Macintosh, the PowerMac G5 stopped being sold in August 2006. The latest version of Mac OS X a PowerPC chip enabled computer was able to run was Mac OS X 10.5 (Leopard) (so long as the computer supported it).

Intel Macs refers to the newer Macintosh computers (since January 2006) that use Intel's CISC processors. Intel Macs uses EFI instead of BIOS and can run the latest versions of Mac OS X. Intel Macs are also able to run PowerPC compiled applications through a translation layer called Rosetta which is optionally installed in 10.6.

If a program is made available as a Universal binary it is able to run on both PPC and Intel Macs however many new applications released today are Intel only (eg. Google Chrome, Final Cut Studio, Mac OS X Snow Leopard).

When it comes to Apple hardware, the differences between the last generation of PowerPC and the first generation of Intel were fairly minor, as far as the end user experience goes. They used the same form factors, and the all-new internals were quite effectively hidden by the unchanged exterior and the accommodations the operating system made for compatibility.

The last PowerPC Macs were sold in 2006, so any new machine since then is Intel.

In general, Intel Macs can run the vast majority of software created for PowerPC Macs. There is a performance hit for the emulation required, but it runs at acceptable speeds even for complex software like Photoshop. PowerPC Macs cannot run Intel software.

The latest version of OS X, Snow Leopard, is available only for Intel-based Macs.

Intel Macs have access to a feature called Boot Camp, which allows them to boot into Windows at full speed. Intel Macs can also run Windows inside virtual machines with the help of third-party software (VMWare Fusion, VirtualBox or Parallels); there is a minor performance penalty for this, but it's much faster than the emulation required for a PowerPC Mac to run Windows software.

The Intel chips at the time of the transition were sourced to be far more thermal and power efficient than the PPC chips of the time. Intel had much more room to grow within the same thermal and physical envelopes in terms of clock rate and the amount of hardware needed to support a given processor choice.

The PPC roadmap was shooting for massive clock rates in the 4 to 5 GHz range which amplified these disadvantages for future PPC chips when compared to future Intel chips.

Moving to Intel processors did away with the need for exotic liquid cooling systems, massive heat sink design and complexity due to space constriants that went into the G5 PowerMac. Power supplies were also downsized.

PPC design was heading directly into mainframe territory with chipkill memory, CPU virtualization, First Failure Data Capture and other high end / high cost features. Just check out this P5 heat sink and 4 processor MPM with associated L3 cache chips to get a feeling for how massive these processors would grow before Power7 manufacturing finally packed more power in a lower clock rate / smaller package. (and this is finally shipping in 2010). Now the Power5 and Power6 are still shipping and awesome at what they do in server land, just not so appropriate for the current Mac market space.

Furthermore, there was nothing coming in the pipeline for a portable processor from PPC so even though the power was there for future desktop machines if one accepts the many tradeoffs already listed. Quite simply, portable macs were starving for horsepower on the PPC architecture and likely drove the urgency of a transition to anything but PPC.

From the end user point of view, you don't need to worry about it much. Many applications were produced as "universal", meaning they run on both PPC and Intel-based Macs, and an emulator (called Rosetta) would let PPC-only apps run on the new Intel machines.

However, as time passed, newer features were only available to Intel Macs, so some applications state outright that they require Intel chips. Also, the latest version of Mac OS X only runs on Intel CPUs.

Apple did a reasonably good job of hiding the entire transition from users, so that everything just kept working as people expected, offloading any heavy lifting to software developers.

Actually, not all PPCs supported little endian mode. In particular the G5 did not. That was not a big deal for most Mac OS X software, since it was only possible to access little endian mode using VMM (Virtual Machine Manager), a feature that was only used Connectix Virtual PC for managing a second address space holding the physical memory of the emulated PC. That was one of the reasons it took so long for Virtual PC to support G5.
– Louis GerbargAug 18 '10 at 3:51

Power PC has its unique set of instruction in which overall is labeled RISC architecture and the way it performs its program goes way faster than that used on PC. About software there isn't difference except the way it was coded or compiled. For example Windows NT 3.51 was developed for PowerPC.

PC most used processor are labeled CISC architecture which change the way you code and the advantage is operates more than a single task at same time.

The term RISC and CISC doesn't make difference since some times RISC 32bits has more complex instructions than CISC 8bits.